Answer:
8 quarters and 14 dimes
Step-by-step explanation:
This situation has two unknowns - the total number of dimes and the total number of quarters. Because we have two unknowns, we will write a system of equations with two equations using the two unknowns.
• [tex]d+q=22[/tex] is an equation representing the total number of coins
• [tex]0.10d+0.25q=3.40[/tex] is an equation representing the total value in money based on the number of coin. 0.10 and 0.25 come from the value of a dime and quarter individually.
We write the first equation in terms of q by subtracting it across the equal sign to get [tex]d=22-q[/tex]. We now substitute this for d in the second equation.
[tex]0.10(22-q)+0.25q=3.40\\2.2-0.10q+0.25q=3.40\\2.2+0.15q=3.40[/tex]
After simplifying, we subtract 2.2 across and divide by the coefficient of q.
[tex]2.2+0.15q=3.40\\0.15q=1.20\\q=8[/tex]
We now know of the 22 coins that 8 are quarters. To find the number of dimes, we subtract 8 from 22 to get 14 dimes.
